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Consecutive primes with ascending or descending differences: Difference between revisions
Consecutive primes with ascending or descending differences (view source)
Revision as of 21:47, 24 May 2021
, 3 years ago→{{header|Nim}}
SqrtNegInf (talk | contribs) (Added Perl) |
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Descending: [322171, 322193, 322213, 322229, 322237, 322243, 322247, 322249] Diffs: [22, 20, 16, 8, 6, 4, 2]
</pre>
=={{header|Nim}}==
<lang Nim>import math, strformat, sugar
const N = 1_000_000
####################################################################################################
# Erathostenes sieve.
var composite: array[2..N, bool] # Initialized to false i.e. prime.
for n in 2..int(sqrt(float(N))):
if not composite[n]:
for k in countup(n * n, N, n):
composite[k] = true
let primes = collect(newSeq):
for n in 2..N:
if not composite[n]: n
####################################################################################################
# Longest sequences.
type Order {.pure.} = enum Ascending, Descending
proc longestSeq(order: Order): seq[int] =
## Return the longest sequence for the given order.
let ascending = order == Ascending
var
currseq: seq[int]
prevPrime = 2
diff = if ascending: 0 else: N
for prime in primes:
let nextDiff = prime - prevPrime
if nextDiff != diff and nextDiff > diff == ascending:
currseq.add prime
else:
if currseq.len > result.len:
result = move(currseq)
currseq = @[prevPrime, prime]
diff = nextDiff
prevPrime = prime
if currseq.len > result.len:
result = move(currseq)
proc `$`(list: seq[int]): string =
## Return the representation of a list of primes with interleaved differences.
var prevPrime: int
for i, prime in list:
if i != 0: result.add &" ({prime - prevPrime}) "
result.addInt prime
prevPrime = prime
echo "For primes < 1000000.\n"
echo "First longest sequence of consecutive primes with ascending differences:"
echo longestSeq(Ascending)
echo()
echo "First longest sequence of consecutive primes with descending differences:"
echo longestSeq(Descending)</lang>
{{out}}
<pre>For primes < 1000000.
First longest sequence of consecutive primes with ascending differences:
128981 (2) 128983 (4) 128987 (6) 128993 (8) 129001 (10) 129011 (12) 129023 (14) 129037
First longest sequence of consecutive primes with descending differences:
322171 (22) 322193 (20) 322213 (16) 322229 (8) 322237 (6) 322243 (4) 322247 (2) 322249</pre>
=={{header|Perl}}==
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